Solve 14c^2+2c

$$14 c ^ { 2 } + 2 c$$

Factor

$$2c\left(7c+1\right)$$

Solution Steps

Factor out 2.

$$2\left(7c^{2}+c\right)$$

Consider 7c^{2}+c. Factor out c.

$$c\left(7c+1\right)$$

Rewrite the complete factored expression.

$$2c\left(7c+1\right)$$

Steps Using the Quadratic Formula

Quadratic polynomial can be factored using the transformation ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where x_{1} and x_{2} are the solutions of the quadratic equation ax^{2}+bx+c=0.

$$14c^{2}+2c=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$c=\frac{-2±\sqrt{2^{2}}}{2\times 14}$$

Take the square root of 2^{2}.

$$c=\frac{-2±2}{2\times 14}$$

Multiply 2 times 14.

$$c=\frac{-2±2}{28}$$

Now solve the equation c=\frac{-2±2}{28} when ± is plus. Add -2 to 2.

$$c=\frac{0}{28}$$

Divide 0 by 28.

$$c=0$$

Now solve the equation c=\frac{-2±2}{28} when ± is minus. Subtract 2 from -2.

$$c=-\frac{4}{28}$$

Reduce the fraction \frac{-4}{28} to lowest terms by extracting and canceling out 4.

$$c=-\frac{1}{7}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 0 for x_{1} and -\frac{1}{7} for x_{2}.

$$14c^{2}+2c=14c\left(c-\left(-\frac{1}{7}\right)\right)$$

Simplify all the expressions of the form p-\left(-q\right) to p+q.

$$14c^{2}+2c=14c\left(c+\frac{1}{7}\right)$$

Add \frac{1}{7} to c by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$14c^{2}+2c=14c\times \frac{7c+1}{7}$$

Cancel out 7, the greatest common factor in 14 and 7.

$$14c^{2}+2c=2c\left(7c+1\right)$$

Evaluate

$$2c\left(7c+1\right)$$